Q 11-06-133JEE MainJEE Main 2022 (26 Jun, Shift 1)Easy
A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2\ \text{rad s}^{-1}$ in a horizontal plane about an axis perpendicular to its plane and passing through the center of the ring. If two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity (in $\text{rad s}^{-1}$)
Answer: (C) $\dfrac{2M}{M+2m}$
No external torque acts, so angular momentum is conserved:
$$MR^2\times2 = (M + 2m)R^2\omega\ \Rightarrow\ \omega = \frac{2M}{M+2m}$$
Solution by Sreeraj P, M.Sc Physics